Question

Упростите выражения:

Answer 1

$1. bigg ( dfrac{a - b}{b} - dfrac{b - a }{a} bigg ) cdot dfrac{b}{a - b} = dfrac{a(a - b) - b(b - a)}{ab} cdot dfrac{b}{a - b} = \ \ \ dfrac{(a^2 - ab - b^2 + ab)b}{ab(a - b)} = dfrac{(a - b)(a + b)}{a(a - b)} = dfrac{a + b}{a}$

$2. bigg ( dfrac{x}{x - a } + dfrac{x}{a} bigg ) : dfrac{x}{x - a } = dfrac{xa + x^2 - xa}{a(x - a)} cdot dfrac{x-a}{x} = dfrac{x^2(x - a)}{a(x - a)x} = \ \ dfrac{x}{a}$